Sulfur is a major antagonist to copper. As you already know, sulfur needs plenty of vitamin C to be metabolized properly. Vitamin C is also a major antagonist of copper. Copper is essentiall to collagen formation.
The problem with most research is supplementation in isolation. Many nutrient complements are needed for proper body functioning. I am not suggesting that you need to supplement copper, only that the results of your referenced study may have been affected by the nutrient balances of the study participants.